Why Estimate?

Date: 09/16/2002 at 18:34:32
From: Doctor Ian
Subject: Re: Estimation
Hi Tyler,
The _point_ of estimating things is that estimating will save you
space, time, or effort, and in return for those savings, you agree to
pay a price in accuracy.
There are lots of different ways to estimate things: you can eliminate
digits from a number (truncation or rounding), you can replace a
decimal number with a fraction (which, technically, is the same
thing), you can replace any number with a 'nearby' number that's
easier to work with, you can use a graph to replace a list of
individual values, you can use a simple function in place of a more
complicated function, and so on.
In each case, you're making a trade-off: "It's not going to hurt much
if my answer is off by a little bit, especially if I can get that
answer ten times more quickly, or by storing a thousand times less
information."
The _art_ of estimating things properly requires two different sets of
skills. The easier one is learning the various techniques of
estimation: rounding, graphing, and so on. The harder one is learning
to recognize how much accuracy you can afford to throw away in a given
situation, and how much benefit you'll get from doing it.
Does this help?
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/